Theory of invariants-based formulation of k⋅p{\bf k}\cdot{\bf p} Hamiltonians with application to strained zinc-blende crystals

Group theoretical methods and ${\bf k}\cdot{\bf p}$ theory are combined to determine spin-dependent contributions to the effective conduction band Hamiltonian. To obtain the constants in the effective Hamiltonian, in general all invariants of the Hamiltonian have to be determined. Hence, we present a systematic approach to keep track of all possible invariants and apply it to the ${\bf k}\cdot{\bf p}$ Hamiltonian of crystals with zinc-blende symmetry, in order to obtain all possible contributions to effective quantities such as effective mass, g-factor and Dresselhaus constant. Further spin-dependent contributions to the effective Hamiltonian arise in the presence of strain. In particular, with regard to the constants $C_3$ and $D$ which describe spin-splitting linear in the components of ${\bf k}$ and ${\boldsymbol\varepsilon}$, considering all possible terms allowed by symmetry is crucial.Comment: 17 pages (preprint style

Multidecadal changes in winter circulation-climate relationship in Europe: frequency variations, within-type modifications, and long-term trends

Using pressure fields classified by the SANDRA algorithm, this study investigates the changes in the relationship between North Atlantic/European sea level pressure (SLP) and gridded European winter (DJF) temperature and precipitation back to 1750. Important changes in the frequency of the SLP clusters are found, though none of them indicating significant long-term trends. However, for the majority of the SLP clusters a tendency toward overall warmer and partly wetter winter conditions is found, most pronounced over the last decades. This suggests important within-type variations, i.e. the temperature and precipitation fields related to a particular SLP pattern change their characteristics over time. Using a decomposition scheme we find for temperature and precipitation that within-type-related variations dominate over those due to changed frequencies of the SLP clusters: Approximately 70% (60%) of European winter temperature (precipitation) variations can be explained by within-type changes, most strongly expressed over Eastern Europe and Scandinavia. This indicates that the current European winter warming cannot be explained by changed frequencies of the SLP patterns alone, but to a larger degree by changed characteristics of the patterns themselves. Potential sources of within-type variations are discusse

Comparison of climate field reconstruction techniques: application to Europe

This paper presents a comparison of principal component (PC) regression and regularized expectation maximization (RegEM) to reconstruct European summer and winter surface air temperature over the past millennium. Reconstruction is performed within a surrogate climate using the National Center for Atmospheric Research (NCAR) Climate System Model (CSM) 1.4 and the climate model ECHO-G 4, assuming different white and red noise scenarios to define the distortion of pseudoproxy series. We show how sensitivity tests lead to valuable "a priori” information that provides a basis for improving real world proxy reconstructions. Our results emphasize the need to carefully test and evaluate reconstruction techniques with respect to the temporal resolution and the spatial scale they are applied to. Furthermore, we demonstrate that uncertainties inherent to the predictand and predictor data have to be more rigorously taken into account. The comparison of the two statistical techniques, in the specific experimental setting presented here, indicates that more skilful results are achieved with RegEM as low frequency variability is better preserved. We further detect seasonal differences in reconstruction skill for the continental scale, as e.g. the target temperature average is more adequately reconstructed for summer than for winter. For the specific predictor network given in this paper, both techniques underestimate the target temperature variations to an increasing extent as more noise is added to the signal, albeit RegEM less than with PC regression. We conclude that climate field reconstruction techniques can be improved and need to be further optimized in future application

Five hundred years of gridded high-resolution precipitation reconstructions over Europe and the connection to large-scale circulation

We present seasonal precipitation reconstructions for European land areas (30°W to 40°E/30-71°N; given on a 0.5°×0.5° resolved grid) covering the period 1500-1900 together with gridded reanalysis from 1901 to 2000 (Mitchell and Jones 2005). Principal component regression techniques were applied to develop this dataset. A large variety of long instrumental precipitation series, precipitation indices based on documentary evidence and natural proxies (tree-ring chronologies, ice cores, corals and a speleothem) that are sensitive to precipitation signals were used as predictors. Transfer functions were derived over the 1901-1983 calibration period and applied to 1500-1900 in order to reconstruct the large-scale precipitation fields over Europe. The performance (quality estimation based on unresolved variance within the calibration period) of the reconstructions varies over centuries, seasons and space. Highest reconstructive skill was found for winter over central Europe and the Iberian Peninsula. Precipitation variability over the last half millennium reveals both large interannual and decadal fluctuations. Applying running correlations, we found major non-stationarities in the relation between large-scale circulation and regional precipitation. For several periods during the last 500years, we identified key atmospheric modes for southern Spain/northern Morocco and central Europe as representations of two precipitation regimes. Using scaled composite analysis, we show that precipitation extremes over central Europe and southern Spain are linked to distinct pressure patterns. Due to its high spatial and temporal resolution, this dataset allows detailed studies of regional precipitation variability for all seasons, impact studies on different time and space scales, comparisons with high-resolution climate models as well as analysis of connections with regional temperature reconstruction

Sensitivity of European glaciers to precipitation and temperature - two case studies

A nonlinear backpropagation network (BPN) has been trained with high-resolution multiproxy reconstructions of temperature and precipitation (input data) and glacier length variations of the Alpine Lower Grindelwald Glacier, Switzerland (output data). The model was then forced with two regional climate scenarios of temperature and precipitation derived from a probabilistic approach: The first scenario ("no change”) assumes no changes in temperature and precipitation for the 2000-2050 period compared to the 1970-2000 mean. In the second scenario ("combined forcing”) linear warming rates of 0.036-0.054°C per year and changing precipitation rates between −17% and +8% compared to the 1970-2000 mean have been used for the 2000-2050 period. In the first case the Lower Grindelwald Glacier shows a continuous retreat until the 2020s when it reaches an equilibrium followed by a minor advance. For the second scenario a strong and continuous retreat of approximately −30m/year since the 1990s has been modelled. By processing the used climate parameters with a sensitivity analysis based on neural networks we investigate the relative importance of different climate configurations for the Lower Grindelwald Glacier during four well-documented historical advance (1590-1610, 1690-1720, 1760-1780, 1810-1820) and retreat periods (1640-1665, 1780-1810, 1860-1880, 1945-1970). It is shown that different combinations of seasonal temperature and precipitation have led to glacier variations. In a similar manner, we establish the significance of precipitation and temperature for the well-known early eighteenth century advance and the twentieth century retreat of Nigardsbreen, a glacier in western Norway. We show that the maritime Nigardsbreen Glacier is more influenced by winter and/or spring precipitation than the Lower Grindelwald Glacie

20th century minimum and maximum temperature variations analysed on a regional scale in Switzerland: statistical analyses of observational data

The major aim of this study is to describe in a detailed manner the 20th century minimum and maximum temperature variations in Switzerland and to assess whether the magnitude of the secular warming and its interannual to interdecadal fluctuations show common seasonal patterns in different climatological regions. In a first step different climatological regions could successfully be established for all four seasons applying a statistical clustering method (Cluster Analysis) to the minimum and maximum temperature time series of a maximum number of climatological stations situated in different parts of the country. A Principal Component Analysis is preceding the actual clustering method which allows to compare the climatological station time series based on minimum and maximum temperature variations as well as on specific station related characteristics. Each of the resulting clusters aggregates a number of climatological stations, which follow a similar temporal development in the temperature data and own comparable station related characteristics. These clusters can therefore be considered as representative of a certain climatological region, which however is not necessarily geographically uniform. The clustering is carried out separately for two different climatological parameters in all four seasons, namely minimum and maximum temperatures in winter, spring, summer and autumn. The resulting clustering patterns reflect a strong dependency upon these climatological parameters as well as upon the seasons. Typical seasonal night-time and day-time temperature distributions over complex terrain have a determining influence on the emerging clustering patterns, which are similar in winter and autumn and in spring and summer. The classic fog and stratus areas combined with the particular cold air drainage over complex terrain have a determining influence on the clustering pattern in winter and autumn and thus the clusters are mainly specified through altitudinal stages. In spring and summer the clustering patterns are still related to the altitude they show however an additional dependency on specific geographical areas. Out of each of the eight clustering patterns three main regions emerged which could be related to the three most contrasting climatic areas in Switzerland and identified as "low altitudes, north", "high altitudes", and "low altitudes, south". The description of the following analyses is restricted to these three regions. The quantitative analyses of the minimum and maximum temperature trends and fluctuations over the 20th century are carried out on regional mean time series computed for each cluster. A new and very detailed description for the seasonal minimum and maximum temperature variations during the 20th century in Switzerland results. Secular warming trends are detected for both, minimum and maximum temperatures. The magnitudes differ mostly between the seasons. The minimum temperatures show generally higher trend estimates than the maximum temperatures with a more pronounced secular warming in winter and autumn. Analysing the temperatures on a decadal scale an abrupt warming is detected during the 1990s, which is especially emphasised for winter minimum temperatures in the region "high altitudes". A further warm period during the 20th century occurred from 1940 to 1950. In contrast to the warming at the end of the century this mid-century warming is most evident in maximum temperatures during spring and summer in the regions "low altitudes, north" and "high altitudes". The long- term decadal trend shows that minimum and maximum temperatures in all regions and seasons except for autumn are persistently increasing since 1980. The autumn temperatures play a special role since their secular warming trend is principally related to rather cold temperatures in the beginning of the century and a mild period during the 1980s, which, however, is not extended into the 1990s. These observations lead to the conclusion that a change in the seasonal warming pattern occurred during the last few decades. Analyses of minimum and maximum temperature extremes are supporting the conclusions formulated above. The warming trends as well as the mild phases, which are observed in minimum and maximum temperatures, can generally be related to a warming in both tails of the distribution (warm and cold). The described results can be linked to the 20th century evolution of large and small scale synoptic systems. The North Atlantic Oscillation exerts a high influence on winter weather types in Switzerland. The increasingly positive North Atlantic Oscillation Index during the last two decades most probably generated a changed frequency pattern of the alpine weather types in winter. In the 1990s this is expressed with a higher frequency of warm winter weather types (convective high-pressure and western advective) on the expenses of a major cold type (eastern advective). The frequency analysis of the alpine weather types for the other seasons does not yield as obvious results as for winter. It was found however, that the main warm periods occurring in different seasons during the century (mid-century summer warming; autumn mild phase in the 1980s) can principally be related to an elevated number of convective high-pressure weather types which usually generate milder temperatures. In an additional chapter the climatological regionalisation method, previously used with temperature data is applied to wind gust data. The analyses show that the gust factor between maximum and mean daily wind speeds over complex terrain follow a lognormal distribution. This knowledge in combination with the climatological regionalisation serves to estimate wind gust speed probabilities over the complex terrain of Switzerland according to three types of synoptic weather situations.Das Hauptziel dieser Studie ist eine möglichst detaillierte Beschreibung der Variationen der Minimum- und Maximumtemperaturen während des 20. Jahrhunderts, wobei es von Interesse ist abzuklären, ob der Umfang der Jahrhunderterwärmung sowie die annuellen und dekadalen Schwankungen in verschiedenen Regionen der Schweiz übereinstimmende saisonale Muster aufweisen. In einem ersten Schritt wurde eine möglichst hohe Anzahl von Minimum- und Maximumtemperaturzeitreihen der Landesklimastationen mit einer statistischen Gruppierungsmethode (Clusterananlyse) erfolgreich nach Jahreszeit geordnet. Vor der eigentlichen Gruppierungsmethode wird eine Hauptkomponentenanylse durchgeführt, die es erlaubt, einen Vergleich der Klimastationen anhand der Variationen in Minimum- und Maximumtemperaturen sowie spezifischen stationsbezogenen Eigenschaften vorzunehmen. In jeder dieser so erhaltenen Gruppen werden Klimastationen vereint, welche ähnliche zeitliche Temperaturvariationen aufweisen und deren stationsbezogenen Eigenschaften vergleichbar sind. Somit können diese Gruppen als jeweilige Vertreter einer bestimmten Klimaregion, deren Gebiet jedoch nicht unbedingt geographisch zusammenhängt, angenommen werden. Die Clusteranalyse wird jeweils auf Minimum- und Maximumtemperatur in den vier verschiedenen Jahreszeiten Winter, Frühling, Sommer und Herbst angewendet. Die daraus resultierenden verschiedenen Gruppierungsmuster widerspiegeln eine starke Abhängigkeit von den Klimaparametern und den Jahreszeiten. Die saisontypische Nachtund Tagestemperaturverteilung über komplexem Terrain übt einen bestimmenden Einfluss aus auf die sich bildenden Gruppierungsmuster, welche im Winter und im Herbst sowie im Frühling und im Sommer am ähnlichsten sind. Während den kühlen Jahreszeiten wird die Gruppierung der Klimastationen von den typischen herbstlichen und winterlichen Nebel- und Stratusgebieten wie auch vom Absinkverhalten der Kaltluft über komplexem Terrain am stärksten beeinflusst. Das Gruppierungsmuster ist daher eng verbunden mit der Höhe über Meer, auf welcher sich eine Klimastation befindet. Während den warmen Jahreszeiten ist die Verbindung zur Höhe immer noch zu finden, die Zugehörigkeit zu einer geographischen Region ist jedoch genauso massgebend. Drei bestimmte Klimaregionen, welche mit den drei gegensätzlichsten Klimazonen in der Schweiz in Verbindung gebracht werden können, treten innerhalb der acht erhaltenen Gruppierungsmuster regelmässig auf. Die drei Regionen werden dementsprechend benannt als: "tiefere Lagen, Nord", "hohe Lagen" und "tiefere Lagen, Süd". Die Beschreibung der Analysen beschränkt sich im weiteren Verlauf der Arbeit auf diese drei Regionen. Die weiteren quantitativen Analysen, welche der Erfassung des Trends in den Minimumund Maximumtemperaturen und deren Schwankungen während des 20. Jahrhunderts dienen, basieren auf mittleren regionalen Zeitreihen, die für jede einzelne Gruppe berechnet werden. Daraus geht eine neue und sehr detaillierte Beschreibung der saisonalen Minimum- und Maximumtemperaturvariationen während des 20. Jahrhunderts hervor. Die Minimum- sowie die Maximumtemperaturen unterliegen einer allgemeinen Erwärmung, welche sich in ihrem Ausmass zwischen den verschiedenen Jahreszeiten am meisten unterscheidet. Die Minimumtemperaturen weisen eine grundsätzlich grössere Erwärmung als die Maximumtemperaturen auf, was sich am stärksten im Winter und im Herbst äussert. Eine dekadal skalierte Untersuchung der Temperaturen lässt darauf schliessen, dass die 90er Jahre einer abrupten Erwärmung unterlagen, welche in den winterlichen Minimumtemperaturen in der Region "hohe Lagen" besonders nachdrücklich ist. Zwischen 1945 und 1950 ist eine weitere Warmphase zu finden, welche im Gegensatz zur Warmphase in den 90er Jahren vor allem in den Maximumtemperaturen des Frühlings und des Sommers in den Regionen "tiefere Lagen, Nord" und "hohe Lagen" ermittelt werden kann. Der dekadal skalierte Langzeittrend weist für alle Regionen und Jahreszeiten, ausser dem Herbst, von 1980 an kontinuierlich ansteigende Temperaturen auf. Die Herbsttemperaturen nehmen eine etwas spezielle Rolle ein, da sie nicht von einer Erwärmung in den 90er Jahren geprägt werden. Die starke Erwärmung, die ihnen über das Jahrhundert hinweg eigen, ist kann vor allem auf kalte Werte am Anfang des Jahrhunderts und eine milde Phase während den 80er Jahren zurückgeführt werden. Diese Beobachtungen lassen auf einen Wandel des jahreszeitlichen Erwärmungsmusters über die letzten Dekaden hinweg schliessen. Die bisher beschriebenen Resultate können auf den Ergebnissen aus der Analyse der Minimum- und Maximumtemperaturextreme abgestützt werden. Die gefundenen Erwärmungstrends sowie die verschiedenen Warmphasen stehen in enger Verbindung mit einer Erwärmung der Extremwerte in beiden Enden (extrem warm und extrem kalt) der Minimum- und Maximumtemperaturverteilung. Die Ergebnisse können in einen direkten Zusammenhang mit der Entwicklung diverser klein- und grossräumiger synoptischer Systeme im 20. Jahrhundert gebracht werden. Die Nordatlantische Oszillation übt einen grossen Einfluss auf die Wetterlagen in der Schweiz während des Winters aus. Mit grosser Wahrscheinlichkeit ist der über die letzten zwei Jahrzehnte hinweg zunehmend positive Nordatlantische Oszillationsindex bezeichnend für einen Wandel im Frequenzenmuster der winterlichen Wetterlagen. Es steht fest, dass während der 90er Jahre ein vermehrtes Auftreten von sogenannten "warmen" winterlichen Wetterlagen, wie konvektive Hochdrucklagen und advektive Westlagen, einhergeht mit einem markanten Rückgang der sogenannten "kalten" winterlichen Wetterlagen wie sie die advektiven Ostlagen darstellen. Die Frequenzanalyse der Wetterlagen in den anderen Jahreszeiten ergibt keine so klaren Resultate. Die grossen Warmphasen während des Jahrhunderts (Sommer Mitte Jahrhundert, Herbst in den 80er Jahren) können jedoch in Verbindung gebracht werden mit einem erhöhten Auftreten von konvektiven Hochdrucklagen, welche für mildere Temperaturen bedeutend sind. In einem zusätzlichen Kapitel wird die klimatologische Regionalisierungsmethode wie sie im vorhergehenden Teil an Temperaturdaten angewendet worden ist an Windgeschwindigkeitsdaten getestet. In der Analyse wird aufgezeigt, dass über komplexem Terrain, der Faktor zwischen den täglichen maximalen und mittleren Windgeschwindigkeiten eine lognormale Verteilung annimmt. In Verbindung mit einer klimatologischen Regionalisierung, welche für drei Arten von synoptischen Wetterlagen vorgenommen wird, dient diese Erkenntnis dazu, die Wahrscheinlichkeit der Windböengeschwindigkeit über dem komplexen Terrain der Schweiz abzuschätzen

A European pattern climatology 1766-2000

Using monthly independently reconstructed gridded European fields for the 500hPa geopotential height, temperature, and precipitation covering the last 235years we investigate the temporal and spatial evolution of these key climate variables and assess the leading combined patterns of climate variability. Seasonal European temperatures show a positive trend mainly over the last 40years with absolute highest values since 1766. Precipitation indicates no clear trend. Spatial correlation technique reveals that winter, spring, and autumn covariability between European temperature and precipitation is mainly influenced by advective processes, whereas during summer convection plays the dominant role. Empirical Orthogonal Function analysis is applied to the combined fields of pressure, temperature, and precipitation. The dominant patterns of climate variability for winter, spring, and autumn resemble the North Atlantic Oscillation and show a distinct positive trend during the past 40years for winter and spring. A positive trend is also detected for summer pattern 2, which reflects an increased influence of the Azores High towards central Europe and the Mediterranean coinciding with warm and dry conditions. The question to which extent these recent trends in European climate patterns can be explained by internal variability or are a result of radiative forcing is answered using cross wavelets on an annual basis. Natural radiative forcing (solar and volcanic) has no imprint on annual European climate patterns. Connections to CO2 forcing are only detected at the margins of the wavelets where edge effects are apparent and hence one has to be cautious in a further interpretatio

A Novel Method for the Homogenization of Daily Temperature Series and Its Relevance for Climate Change Analysis

Instrumental daily series of temperature are often affected by inhomogeneities. Several methods are available for their correction at monthly and annual scales, whereas few exist for daily data. Here, an improved version of the higher-order moments (HOM) method, the higher-order moments for autocorrelated data (HOMAD), is proposed. HOMAD addresses the main weaknesses of HOM, namely, data autocorrelation and the subjective choice of regression parameters. Simulated series are used for the comparison of both methodologies. The results highlight and reveal that HOMAD outperforms HOM for small samples. Additionally, three daily temperature time series from stations in the eastern Mediterranean are used to show the impact of homogenization procedures on trend estimation and the assessment of extremes. HOMAD provides an improved correction of daily temperature time series and further supports the use of corrected daily temperature time series prior to climate change assessment

Characterisation of extreme winter precipitation in Mediterranean coastal sites and associated anomalous atmospheric circulation patterns

We present an analysis of daily extreme precipitation events for the extended winter season (October–March) at 20 Mediterranean coastal sites covering the period 1950–2006. The heavy tailed behaviour of precipitation extremes and estimated return levels, including associated uncertainties, are derived applying a procedure based on the Generalized Pareto Distribution, in combination with recently developed methods. Precipitation extremes have an important contribution to make seasonal totals (approximately 60% for all series). Three stations (one in the western Mediterranean and the others in the eastern basin) have a 5-year return level above 100 mm, while the lowest value (estimated for two Italian series) is equal to 58 mm. As for the 50-year return level, an Italian station (Genoa) has the highest value of 264 mm, while the other values range from 82 to 200 mm. Furthermore, six series (from stations located in France, Italy, Greece, and Cyprus) show a significant negative tendency in the probability of observing an extreme event. The relationship between extreme precipitation events and the large scale atmospheric circulation at the upper, mid and low troposphere is investigated by using NCEP/NCAR reanalysis data. A 2-step classification procedure identifies three significant anomaly patterns both for the western-central and eastern part of the Mediterranean basin. In the western Mediterranean, the anomalous southwesterly surface to mid-tropospheric flow is connected with enhanced moisture transport from the Atlantic. During ≥5-year return level events, the subtropical jet stream axis is aligned with the African coastline and interacts with the eddy-driven jet stream. This is connected with enhanced large scale ascending motions, instability and leads to the development of severe precipitation events. For the eastern Mediterranean extreme precipitation events, the identified anomaly patterns suggest warm air advection connected with anomalous ascent motions and an increase of the low- to mid-tropospheric moisture. Furthermore, the jet stream position (during ≥5-year return level events) supports the eastern basin being in a divergence area, where ascent motions are favoured. Our results contribute to an improved understanding of daily precipitation extremes in the cold season and associated large scale atmospheric features